Pith Number

pith:SP4JAFFH

pith:2009:SP4JAFFHHRQJKAAULRJR5HJYQR

not attested not anchored not stored refs pending

About the blowup of quasimodes on Riemannian manifolds

Christopher D. Sogge, John A. Toth, Steve Zelditch

arxiv:0908.0688 v1 · 2009-08-05 · math.AP · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SP4JAFFHHRQJKAAULRJR5HJYQR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:35:26.705788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93f89014a73c609500145c531e9d388460b8d813211ad570cf7d485afc03e1b8

Aliases

arxiv: 0908.0688 · arxiv_version: 0908.0688v1 · doi: 10.48550/arxiv.0908.0688 · pith_short_12: SP4JAFFHHRQJ · pith_short_16: SP4JAFFHHRQJKAAU · pith_short_8: SP4JAFFH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SP4JAFFHHRQJKAAULRJR5HJYQR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 93f89014a73c609500145c531e9d388460b8d813211ad570cf7d485afc03e1b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69eaf461e0adbc46d2062bb9eb98aa8a5c1d96c75f03fe878539831186e40a17",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-08-05T15:31:38Z",
    "title_canon_sha256": "d1bc2b976d35031f7b3cdebe6c55b507d0722344dddfd49d1ed0498393b7d76d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.0688",
    "kind": "arxiv",
    "version": 1
  }
}